A294488 Numbers k such that (73*10^k - 91)/9 is prime.

1, 3, 4, 6, 7, 10, 63, 84, 181, 186, 205, 235, 426, 612, 3379, 4203, 4410, 9091, 12640, 26386, 39069, 45451

Offset

1,2

Comments

For k>1, numbers such that the digit 8 followed by k-2 occurrences of the digit 1 followed by the digits 01 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 81w01.

Example

3 is in this sequence because (73*10^3 - 91)/9 = 8101 is prime.
Initial terms and primes associated:
a(1) = 1, 71;
a(2) = 3, 8101;
a(3) = 4, 81101;
a(4) = 6, 8111101;
a(5) = 7, 81111101; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(73*10^# - 91)/9] &]
ParallelMap[If[PrimeQ[(73*10^# - 91)/9], #, Nothing] &, Range@100000] (* Robert G. Wilson v, Oct 31 2017 *)

Prog

(PARI) isok(n) = isprime((73*10^n - 91)/9); \\ Michel Marcus, Nov 01 2017

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A108588 A194095 A064404 * A364341 A335059 A047514

Adjacent sequences: A294485 A294486 A294487 * A294489 A294490 A294491

Keyword

nonn,more,hard

Author

Robert Price, Oct 31 2017

Status

approved